The interactions between cells and their surrounding environments have been receiving increased attention over the past twenty years. Cell-substrate interactions can profoundly affect cell behavior, including adhesion, spreading, migration, division, differentiation, apoptosis, and internal cellular signaling. The binding interactions between cells and their material layer(s) are influenced by mechanical stimuli, such as material stiffness and material curvatures. The effects of material stiffness on cell behaviors have been extensively studied (Alenghat and Ingber, 2002; Wang et al., 2002; Janmey and Weitz, 2004; Yeung et al., 2004; Engler et al., 2004; Chen et al., 2004; Wong et al., 2004; Brown et al., 2006; Engler et al., 2006; Kasza et al., 2007; Rodriguez et al., 2013); however, the cellular responses to the geometry of a substrate, e.g., the curvature of the substrate, are not well-documented (Chen et al., 1997; Sniadecki et al., 2006; Sanz-Herrera et al., 2009; Digabel et al., 2010; Baker and Chen, 2012). Since the materials on which the cells grow in vivo are normally not flat, the responses of cells to material curvatures should also be a fundamental aspect of cell mechanosensitivity and mechanotransduction. The importance of material curvature effects on cell behaviors can be illustrated by understanding the process of cell attachment and growth on curved surfaces of bones and implants in vivo.
Normal cell natural spreading is random in every direction, and the resulting cell spread shape is irregular and non-uniform (Alberts et al., 2015). Two-dimensional (2D) geometric patterns and chemical patterns have been widely generated by microfabrication technologies to define the spread shapes of living cells in in vitro cultures, which has opened many opportunities for and re-shaped the area of cellular bioengineering and mechanobiology (Kilian et al, 2010; Wan et al., 2010; Tang et al., 2012; Tao et al., 2013). Cell isotropic-spreading, where the resulting cell outline or boundary is roughly circular and smooth which means the extent of the cell spreading in every direction is roughly the same from the geometric center of the cell, has been realized by culturing the cells in geometrically-patterned and chemically-patterned circular areas (Chen et al., 1997; Liu and Chen, 2007; Song et al., 2011), but the geometric patterning and or the chemical patterning must be there to control or restrict the spreading of a cell to realize the cell isotropic-spreading, which means the realized cell isotropic-spreading is not a cell natural spreading. Therefore, it is difficult to take advantage of or use cell isotropic-spreading realized by culturing cells in geometrically-patterned and chemically-patterned circular areas for studies and applications in cellular bioengineering and mechano-biology.
Further, in response to geometrical stimuli cells change their morphologies and motilities, and these changes are most likely caused by the changes in the intracellular forces associated with the changes in the cell focal adhesions and actin stress fibers due to the geometrical stimuli (Folch and Toner, 2000; Discher et al., 2005; Georges and Janmey, 2005; Vogel and Sheetz, 2006; Vartanian et al., 2008; Cheng et al., 2009; Wan et al., 2010; Rape et al., 2011; Song et al., 2011; Yao et al., 2013; Meehan and Nain, 2014). The geometry of a substrate also determines the orientation and rate of cell growth (Smeal et al., 2005; Rumpler et al., 2008; Hwang et al., 2009; Veiseh et al., 2015; Viswanathan et al., 2015; Zadpoor, 2015).